... | ... | @@ -14,7 +14,7 @@ where $`N`$ is the number of pixels inside the ROI. As an example, the top-left |
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![demo1](uploads/6a5c9c83f30e1cd99837e8d869de385b/demo1.png)
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Although vector forces on contacts of discs can be solved by the [nonlinear fitting algorithm](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/inverse-analysis), $`G^2`$ method remains a popular choice to estimate stress based on photoelastic fringes because the following reasons: (1) $`G^2`$ calculation runs much faster (2) $`G^2`$ works for relatively low resolutions and (3) $`G^2`$ does not rely on the initial guess of contact forces, which can be a problem for the vector force fitting algorithm. For example, the right figure above shows the fit error for diametrically loaded disc under different loading force (real force) and using different initial guess force for the nonlinear force fitting algorithm. It is clear that only when the gauss force is close to the real force that the fitting algorithm gives accurate results.
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Although vector forces on contacts of discs can be solved by the [nonlinear fitting algorithm](/inverse-analysis), $`G^2`$ method remains a popular choice to estimate stress based on photoelastic fringes because the following reasons: (1) $`G^2`$ calculation runs much faster (2) $`G^2`$ works for relatively low resolutions and (3) $`G^2`$ does not rely on the initial guess of contact forces, which can be a problem for the vector force fitting algorithm. For example, the right figure above shows the fit error for diametrically loaded disc under different loading force (real force) and using different initial guess force for the nonlinear force fitting algorithm. It is clear that only when the gauss force is close to the real force that the fitting algorithm gives accurate results.
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## 2. Global scale stress indicator: boundary pressure
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... | ... | @@ -25,7 +25,7 @@ On global scale, calibrations show that $`G^2`$ depends linearly on boundary pre |
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## 3. Particle scale stress indicator: sum of force magnitude
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### 3.1. Comparison between $`G^2`$ and light intensity $`I`$
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On single particle scale, $`G^2`$ is shown to be proportional to the summation of the magnitudes of the contact forces acting on the particle [4]. $`G^2`$ can measure larger forces than [the intensity measurement](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/qualitative-analysis) when the resolution is high enough. The figure below show the evolution of $`G^2`$ and average light intensity $`I`$ inside a numerical simulated disc. The horizontal axis is the diametric loading force. It is clear that $`G^2`$ saturates at a much larger force than the average light intensity $`I`$. So $`G^2`$ is a better stress indicator at particle scale than $`I`$ if the resolution is not extremely low.
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On single particle scale, $`G^2`$ is shown to be proportional to the summation of the magnitudes of the contact forces acting on the particle [4]. $`G^2`$ can measure larger forces than [the intensity measurement](/qualitative-analysis) when the resolution is high enough. The figure below show the evolution of $`G^2`$ and average light intensity $`I`$ inside a numerical simulated disc. The horizontal axis is the diametric loading force. It is clear that $`G^2`$ saturates at a much larger force than the average light intensity $`I`$. So $`G^2`$ is a better stress indicator at particle scale than $`I`$ if the resolution is not extremely low.
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![demo3](uploads/f7e74b25aaea4c0e3d52793c5e2e8c6c/demo3.png)
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... | ... | @@ -59,4 +59,4 @@ The discussion so far only considered disc particles. An unproved empirical expe |
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[<go back to home](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home) |
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[<go back to home](/home) |
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\ No newline at end of file |